Algebra 1B: Unit 1 Obj 4 Power To A Power

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| By Vicki Barr

Vicki Barr

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Quizzes Created: 14 | Total Attempts: 2,456

| Attempts: 132

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Easy First Hard First Sequential

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1/10 Questions

When you have which variable does the 5 go to?
- The x
- The y
- Both x and y
- Neither x or y

About This Quiz

This Algebra 1B quiz assesses the ability to simplify exponential expressions using the power to a power rule. Key skills include simplifying expressions like (52)3 and (x7)4, enhancing understanding of exponent rules crucial for algebra proficiency.

Algebra 1b: Unit 1 Obj 4 Power To A Power - Quiz

2.

Which choice represents the simplified exponential expression? (z⁵)⁸
- Z^-3
- Z
- Z^13
- Z^40
Correct Answer

A. 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.

Which choice represents the simplified exponential expression? (x⁷)⁴
- X^11
- X
- X^28
- X^3
Correct Answer

A. 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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4.

(xy)⁴ * (xy)² = x⁶ * y⁶
- True
- False
Correct Answer

A. True

Explanation

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

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5.

Simplify
- -9x^6y^3
- 9x^5y^2
- 9x^6y^2
- -9x^5y^2
Correct Answer

A. 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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6.

Which choice represents the simplified exponential expression?
- 7^6
- 7^8
- 7^2
- 117649
- 5764801
Correct Answer

A. 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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7.

Which choice represents the simplified exponential expression?(5²)³
- 5^5
- 5^-6
- 5^6
- 25^3
- 15625
- 3125
Correct Answer

A. 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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8.
- (64g^12h^10)/(25f^6)
- (64g^8h^7)/(25f^5)
- (27g^12h^10)/(f^6)
- (729g^8h^7)/(f^5)
- (8g^12h^10)/(5f^6)
Correct Answer

A. (64g^12h^10)/(25f^6)
9.

Which choice represents the simplified exponential expression?(s ^-6)⁹
- S
- S^3
- S^ -15
- S^ -54
- 1/s^54
- 1/s^3
- S^-3
Correct Answer

A. 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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10.
- 1/81a^16b^28
- B^28/(81a^16)
- 81b^28/(a^16)
- B^11/-81a^0
- -81b^28/b^16
- 81a^-16b^28
- 81/a^16b^28
Correct Answer

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