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Popular >

simplify (-3/2)^7*(-2/3)^4

Solution

simplify

(- \frac{3}{2})^{7} \cdot (- \frac{2}{3})^{4}

Solution

- \frac{27}{8}

+1

Decimal Notation

- 3.375

Solution steps

(- \frac{3}{2})^{7} (- \frac{2}{3})^{4}

(- \frac{3}{2})^{7} = - \frac{2187}{128}

= - \frac{2187}{128} (- \frac{2}{3})^{4}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

(- \frac{2}{3})^{4} = (\frac{2}{3})^{4}

= - \frac{2187}{128} (\frac{2}{3})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{2}{3})^{4} = \frac{2 ^{4}}{3 ^{4}}

= - \frac{2187}{128} \cdot \frac{2 ^{4}}{3 ^{4}}

2^{4} = 16

= - \frac{2187}{128} \cdot \frac{16}{3 ^{4}}

3^{4} = 81

= - \frac{2187}{128} \cdot \frac{16}{81}

- \frac{2187}{128} \cdot \frac{16}{81} = - \frac{27}{8}

= - \frac{27}{8}

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Frequently Asked Questions (FAQ)

What is (-3/2)^7*(-2/3)^4 ?
The solution to (-3/2)^7*(-2/3)^4 is -27/8