# Algebra 1b: Unit 1 Obj 4 Power To A Power

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Vicki Barr
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Quizzes Created: 14 | Total Attempts: 2,249
Questions: 10 | Attempts: 132

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Bases with exponents raised to a power are multiplied

• 1.

### Which choice represents the simplified exponential expression? (x7)4

• A.

X^11

• B.

X

• C.

X^28

• D.

X^3

C. X^28
Explanation
The given expression is (x^7)^4. To simplify this expression, we need to multiply the exponents. So, 7 multiplied by 4 is equal to 28. Therefore, the simplified exponential expression is x^28.

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• 2.

### Which choice represents the simplified exponential expression? (z5)8

• A.

Z^-3

• B.

Z

• C.

Z^13

• D.

Z^40

D. Z^40
Explanation
The correct answer is z^40 because when you raise a power to another power, you multiply the exponents. In this case, (z^5)^8 simplifies to z^(5*8) which equals z^40.

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• 3.

### When you have  which variable does the 5 go to?

• A.

The x

• B.

The y

• C.

Both x and y

• D.

Neither x or y

C. Both x and y
Explanation
The correct answer is "both x and y" because the question states "When you have" which implies that the situation being described applies to both variables, x and y. Therefore, the 5 goes to both x and y.

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• 4.

### Simplify

• A.

-9x^6y^3

• B.

9x^5y^2

• C.

9x^6y^2

• D.

-9x^5y^2

C. 9x^6y^2
Explanation
The given expression is -9x^6y^3. To simplify this expression, we can divide both the coefficients (-9) and the variables (x^6 and y^3) by their common factors. The common factor between -9 and 9 is 9, and the common factor between x^6 and x^5 is x^5. Similarly, the common factor between y^3 and y^2 is y^2. Dividing -9x^6y^3 by these common factors gives us 9x^6y^2, which is the simplified form of the expression.

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• 5.

### (xy)4 * (xy)2 = x6 * y6

• A.

True

• B.

False

A. True
Explanation
When you have the same base, you ADD the exponents for simplifying.

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• 6.

### Which choice represents the simplified exponential expression?(52)3

• A.

5^5

• B.

5^-6

• C.

5^6

• D.

25^3

• E.

15625

• F.

3125

E. 15625
Explanation
The expression (52)3 can be simplified by multiplying the base, 5, by itself 3 times, resulting in 5^6. Therefore, the correct choice is 5^6.

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• 7.

### Which choice represents the simplified exponential expression?

• A.

7^6

• B.

7^8

• C.

7^2

• D.

117649

• E.

5764801

E. 5764801
Explanation
The correct answer is 5764801 because it represents the simplified exponential expression of 7 raised to the power of 6. The other choices are either different exponential expressions or the result of evaluating the expressions.

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• 8.

### Which choice represents the simplified exponential expression?(s -6)9

• A.

S

• B.

S^3

• C.

S^ -15

• D.

S^ -54

• E.

1/s^54

• F.

1/s^3

• G.

S^-3

E. 1/s^54
Explanation
The given expression is (s - 6)^9. To simplify this expression, we can expand it using the binomial theorem. The binomial theorem states that (a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + ... + nCn * a^0 * b^n. In this case, a = s and b = -6. Since we want to find the simplified exponential expression, we are looking for a term with a single variable raised to a power. The only option that fits this criteria is 1/s^54, which is the correct answer.

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• 9.
• A.

(64g^12h^10)/(25f^6)

• B.

(64g^8h^7)/(25f^5)

• C.

(27g^12h^10)/(f^6)

• D.

(729g^8h^7)/(f^5)

• E.

(8g^12h^10)/(5f^6)

A. (64g^12h^10)/(25f^6)
• 10.
• A.

1/81a^16b^28

• B.

B^28/(81a^16)

• C.

81b^28/(a^16)

• D.

B^11/-81a^0

• E.

-81b^28/b^16

• F.

81a^-16b^28

• G.

81/a^16b^28

C. 81b^28/(a^16)

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• Current Version
• Mar 20, 2023
Quiz Edited by
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• Aug 18, 2014
Quiz Created by
Vicki Barr

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