Question

Which expression is equivalent to (x Superscript 27 Baseline y) Superscript one-third?.

Answer 1

Answer:

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Step-by-step explanardgdrttion:

Answer 2

To solve the problem we must know the basic exponential properties.

What are the basic exponent properties?

${a^m} \cdot {a^n} = a^{(m+n)}$

$\dfrac{a^m}{a^n} = a^{(m-n)}$

$\sqrt[m]{a^n} = a^{\frac{n}{m}}$

$(a^m)^n = a^{m\times n}$

$(m\times n)^a = m^a\times n^a$

The expression can be written as $x^9\sqrt[3]{y}$.

Given to us

• $(x^{27}y)^\frac{1}{3}$

$(x^{27}y)^\frac{1}{3}$

Using the exponential property$(m\times n)^a = m^a\times n^a$,

$=(x^{27}y)^\frac{1}{3}\\\\=x^{\frac{27}{3}}\times y^\frac{1}{3}\\\\=x^9\times y^\frac{1}{3}$

Using the exponential property $\sqrt[m]{a^n} = a^{\frac{n}{m}}$,

$=x^9\times y^\frac{1}{3}\\\\=x^9\times \sqrt[3]{y}\\\\=x^9 \sqrt[3]{y}$

Hence, the expression can be written as $x^9\sqrt[3]{y}$.

Learn more about Exponent properties:

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