Math Questions: Laws Of Exponents And Algebraic Fractions

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| Attempts: 3,569 | Questions: 17 | Updated: Mar 22, 2025
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1) The result of simplifying the expression  (x 3 y 4 ) 3   is

Explanation

Multiply the power of x by 3 from the outside of the expression to get x^9. Multiply the power of y by 3 from the outside to get y^12

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About This Quiz
Math Questions: Laws Of Exponents And Algebraic Fractions - Quiz

This quiz focuses on the laws of exponents and algebraic fractions, assessing understanding of exponent rules and simplification of expressions involving exponents and algebraic terms. It's designed to enhance learners' skills in algebraic manipulations.

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2) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«/math»

Explanation

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3) (a4)6 = 

Explanation

The given expression (a4)6 can be simplified by multiplying the two numbers within the parentheses first. Since there is no variable or operation between the parentheses and the number 4, we can assume that it is a multiplication operation. Therefore, (a4)6 is equivalent to 4 * 6, which is 24.

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4) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/mfenced»«mn»3«/mn»«/msup»«/math»

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5) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»a«/mi»«mn»7«/mn»«/msup»«msup»«mi»c«/mi»«mn»3«/mn»«/msup»«/mrow»«mrow»«msup»«mi»a«/mi»«mn»7«/mn»«/msup»«mi»c«/mi»«/mrow»«/mfrac»«/math»

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6) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»a«/mi»«mn»5«/mn»«/msup»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/mfrac»«/math»

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7) What is the answer to [(x 4 y 5)] 0  

Explanation

The given answer "one, 1" suggests that the expression [(x 4 y 5)] 0 evaluates to both the word "one" and the number 1. However, without any context or further information about the expression or the variables x and y, it is not possible to determine the exact meaning or value of the expression. Therefore, the explanation for this answer is not available.

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8) (3a4)2 =

Explanation

The given expression, (3a4)2, can be simplified by first evaluating the exponent, which is 2. This means that the expression inside the parentheses, 3a4, needs to be squared. To square this expression, we multiply it by itself. So, (3a4)2 = (3a4) x (3a4) = 9a8.

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9) Ac4 x a3c2 = 

Explanation

The given expression "ac4 x a3c2" represents the multiplication of the terms "ac4" and "a3c2". In this expression, "ac4" means "a" multiplied by "c" multiplied by 4, and "a3c2" means "a" multiplied by 3 multiplied by "c" squared. To multiply these terms, we can multiply the coefficients (4 and 3) together to get 12, and multiply the variables (a and c) together to get "a" multiplied by "c". Therefore, the result of the expression is 12ac.

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10) A3 x a2 = 

Explanation

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11) 4a3 x 3a5 = 

Explanation

The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables. Therefore, 4a3 x 3a5 is equal to 12a8.

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12) X 4 x 3  will result in an exponent of

Explanation

The expression "x 4 x 3" can be simplified as "x^4 * x^3". When multiplying two powers with the same base, you add the exponents. In this case, the base is "x" and the exponents are 4 and 3. So, the sum of the exponents is 7, resulting in an exponent of 7 for the expression.

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13) (2a3c5)3 = 

Explanation

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14) All bases have an exponent

Explanation

When a base has no exponent written it is assumed to be 1, thus all bases have an exponent even if none is written.

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15) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«msup»«mi»a«/mi»«mn»5«/mn»«/msup»«/mfrac»«/math»

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16) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»4«/mn»«msup»«mi»a«/mi»«mn»5«/mn»«/msup»«msup»«mi»c«/mi»«mn»3«/mn»«/msup»«/mrow»«mrow»«mn»16«/mn»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«msup»«mi»c«/mi»«mn»4«/mn»«/msup»«/mrow»«/mfrac»«/math»

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17) «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»21«/mn»«msup»«mi»a«/mi»«mn»3«/mn»«/msup»«/mrow»«mrow»«mn»7«/mn»«msup»«mi»a«/mi»«mn»4«/mn»«/msup»«/mrow»«/mfrac»«/math»

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The result of simplifying the expression  (x 3 y 4 )...
(a4)6 = 
What is the answer to [(x 4 y 5)] 0  
(3a4)2 =
Ac4 x a3c2 = 
A3 x a2 = 
4a3 x 3a5 = 
X 4 x 3  will result in an exponent of
(2a3c5)3 = 
All bases have an exponent
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