Which expressions are equivalent to (b^(2))^((1)/(9)) ? Choose all answers that apply: A (b^(-(1)/(9)))^(2) B (b^((1)/(9)))^(2) c. (b^((1)/(2)))^(9) D None of the above

Determine Exponent Simplification: We need to determine which of the given options are equivalent to the expression (b^(2))^((1)/(9)). According to the properties of exponents, when we raise a power to another power, we multiply the exponents. So, (b^(2))^((1)/(9)) simplifies to b^(2*(1/9)), which is b^(2/9).Evaluate Option A: Now let's evaluate each option to see if it simplifies to b^(2/9). Option A: (b^(-(1)/(9)))^(2) simplifies to b^(-2/9), which is not equivalent to b^(2/9) because the exponent is negative.Evaluate Option B: Option B: (b^((1)/(9)))^(2) simplifies to b^(2/9), which is equivalent to our original expression (b^(2))^((1)/(9)).Evaluate Option C: Option C: (b^((1)/(2)))^(9) simplifies to b^(9/2), which is not equivalent to b^(2/9) because the exponent is much larger and not a reciprocal.Evaluate Option D: Option D: None of the above is not correct because we have found that Option B is equivalent to the original expression.

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Which expressions are equivalent to
(b^(2))^((1)/(9)) ?
Choose all answers that apply:
A
(b^(-(1)/(9)))^(2)
B
(b^((1)/(9)))^(2)
c.
(b^((1)/(2)))^(9)
D None of the above

Which expressions are equivalent to $\left(b^{2}\right)^{\frac{1}{9}}$ ? $\newline$ Choose all answers that apply: $\newline$ A $\left(b^{-\frac{1}{9}}\right)^{2}$ $\newline$ B $\left(b^{\frac{1}{9}}\right)^{2}$ $\newline$ C $\left(b^{\frac{1}{2}}\right)^{9}$ $\newline$ D None of the above

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which expressions are equivalent to

\left(b^{2}\right)^{\frac{1}{9}}

\newline

Choose all answers that apply:

\newline

\left(b^{-\frac{1}{9}}\right)^{2}

\newline

\left(b^{\frac{1}{9}}\right)^{2}

\newline

\left(b^{\frac{1}{2}}\right)^{9}

\newline

D None of the above

Determine Exponent Simplification: We need to determine which of the given options are equivalent to the expression $(b^{2})^{(\frac{1}{9})}$ . According to the properties of exponents, when we raise a power to another power, we multiply the exponents. So, $(b^{2})^{(\frac{1}{9})}$ simplifies to $b^{2*(\frac{1}{9})}$ , which is $b^{\frac{2}{9}}$ .
Evaluate Option A: Now let's evaluate each option to see if it simplifies to $b^{\frac{2}{9}}$ . $\newline$ Option A: $(b^{-\left(\frac{1}{9}\right)})^{2}$ simplifies to $b^{-\frac{2}{9}}$ , which is not equivalent to $b^{\frac{2}{9}}$ because the exponent is negative.
Evaluate Option B: Option B: $(b^{(1/9)})^{2}$ simplifies to $b^{2/9}$ , which is equivalent to our original expression $(b^{2})^{(1/9)}$ .
Evaluate Option C: Option C: $(b^{(1/2)})^{9}$ simplifies to $b^{9/2}$ , which is not equivalent to $b^{2/9}$ because the exponent is much larger and not a reciprocal.
Evaluate Option D: Option D: None of the above is not correct because we have found that Option B is equivalent to the original expression.