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

1) When you have

which variable does the 5 go to?

The x

The y

Both x and y

Neither x or y

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.

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.

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

Z^-3

Z

Z^13

Z^40

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.

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.

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

X^11

X

X^28

X^3

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.

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.

4) (xy)⁴ * (xy)² = x⁶ * y⁶

True

False

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

Explanation

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

5) Simplify

-9x^6y^3

9x^5y^2

9x^6y^2

-9x^5y^2

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.

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.

6) Which choice represents the simplified exponential expression?

open parentheses 7 to the power of 4 close parentheses squared

7^6

7^8

7^2

117649

5764801

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.

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.

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

5^5

5^-6

5^6

25^3

15625

3125

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.

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.

8)

open parentheses fraction numerator 72 f to the power of 4 g to the power of 9 h to the power of 5 over denominator 45 f to the power of 7 g cubed end fraction close parentheses squared

(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)

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Explanation

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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

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.

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.