What is (2^4a^9)(2^{-2}a^{-3}) ?

The solution to (2^4a^9)(2^{-2}a^{-3}) is 4a^6

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simplify (2^4a^9)(2^{-2}a^{-3})

simplify

(2^{4} a^{9}) (2^{- 2} a^{- 3})

4 a^{6}

Solution steps

(2^{4} a^{9}) (2^{- 2} a^{- 3})

2^{4} = 16

= 16 a^{9} \cdot 2^{- 2} a^{- 3}

2^{- 2} = \frac{1}{4}

= 16 a^{9} \frac{1}{4} a^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

a^{- 3} = \frac{1}{a ^{3}}

= 16 a^{9} \frac{1}{4} \cdot \frac{1}{a ^{3}}

Apply the fraction rule:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{16 a ^{9} \cdot 1 \cdot 1}{4 a ^{3}}

Multiply the numbers:

16 \cdot 1 \cdot 1 = 16

= \frac{16 a ^{9}}{4 a ^{3}}

Factor the number:

16 = 4 \cdot 4

= \frac{4 \cdot 4 a ^{9}}{4 a ^{3}}

Cancel the common factor:

4

= \frac{4 a ^{9}}{a ^{3}}

Simplify

\frac{a ^{9}}{a ^{3}} : a^{6}

= 4 a^{6}

[\frac{( 7 x ^{3} y z ^{5} ) ^{6}}{( 49 x ^{6} y ^{2} z ^{4} ) ^{3}}]^{4}

\frac{( x ^{5} + y ^{5} )}{( x + y )}