Test your understanding of exponents quiz!

1) Any base raised to this power will equal one

Any number raised to the power of zero equals one. Therefore, any base raised to the power of zero will also equal one.

Explanation

Any number raised to the power of zero equals one. Therefore, any base raised to the power of zero will also equal one.

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2) The result of simplifying the expression (x ³ y ⁴ ) ³ is

X^9 y^12

(xy)^10

Y

(xy)^21

X^6 y^7

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

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

3) All bases have an exponent

True

False

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

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.

4) [(x ⁴ y ⁵) ^-3 - (x ⁵) ^-3/2] ⁰

The given expression is [(x^4 * y^5) - 3 - (x^5) - (3/2)] * 0. When any number is multiplied by 0, the result is always 0. Therefore, no matter what the values of x and y are, the entire expression will evaluate to 0. Hence, the answer is 0.

Explanation

The given expression is [(x^4 * y^5) - 3 - (x^5) - (3/2)] * 0. When any number is multiplied by 0, the result is always 0. Therefore, no matter what the values of x and y are, the entire expression will evaluate to 0. Hence, the answer is 0.

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5) If a number has no power written then the power is assumed to be

0

-1

1

None, it simply has no power

All numbers without a power have an exponent of 1. Example 5 is the same as 5^1

Explanation

All numbers without a power have an exponent of 1. Example 5 is the same as 5^1

6) The exponents of exponential expressions with different bases can be added together.

True

False

The terms x^3 and y^4 cannot be combined into one term as there is no common base.

Explanation

The terms x^3 and y^4 cannot be combined into one term as there is no common base.

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

The expression x^4 x 3 is equivalent to x^(4+3), which simplifies to x^7. In other words, when you multiply x to the power of 4 by 3, you are effectively multiplying x by itself 4 times and then multiplying the result by x two more times. This results in x being multiplied by itself a total of 7 times, giving us x^7.

Explanation

The expression x^4 x 3 is equivalent to x^(4+3), which simplifies to x^7. In other words, when you multiply x to the power of 4 by 3, you are effectively multiplying x by itself 4 times and then multiplying the result by x two more times. This results in x being multiplied by itself a total of 7 times, giving us x^7.

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8) "Cross the line Change the sign" refers to simplifying what type of exponential expressions

Power of a Power

Product of Powers

Quotient of Powers

Negative exponents

Zero Property

"Cross the line Change the sign" refers to simplifying negative exponents. When we have a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent. For example, if we have 2^-3, we can rewrite it as 1/(2^3). This rule allows us to convert negative exponents into positive exponents, which makes calculations and simplifications easier.

Explanation

"Cross the line Change the sign" refers to simplifying negative exponents. When we have a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent. For example, if we have 2^-3, we can rewrite it as 1/(2^3). This rule allows us to convert negative exponents into positive exponents, which makes calculations and simplifications easier.

9) There is no fundemental mathematical truth for what 0 ⁰ is equal to

True

False

The statement is true because in mathematics, division by zero is undefined. When dividing any number by zero, there is no meaningful result or value that can be assigned. Therefore, there is no fundamental mathematical truth for what 0 divided by 0 is equal to.

Explanation

The statement is true because in mathematics, division by zero is undefined. When dividing any number by zero, there is no meaningful result or value that can be assigned. Therefore, there is no fundamental mathematical truth for what 0 divided by 0 is equal to.

Test Your Understanding Of Exponents Quiz!