What is (16x^2y^4)(1/4 x^5y) ?

The solution to (16x^2y^4)(1/4 x^5y) is 4x^7y^5

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simplify (16x^2y^4)(1/4 x^5y)

simplify

(16 x^{2} y^{4}) (\frac{1}{4} x^{5} y)

4 x^{7} y^{5}

Solution steps

(16 x^{2} y^{4}) (\frac{1}{4} x^{5} y)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{2} x^{5} = x^{2 + 5}

= 16 y^{4} \frac{1}{4} x^{2 + 5} y

Add the numbers:

2 + 5 = 7

= 16 y^{4} \frac{1}{4} x^{7} y

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

y^{4} y = y^{4 + 1}

= 16 \cdot \frac{1}{4} x^{7} y^{4 + 1}

Add the numbers:

4 + 1 = 5

= 16 \cdot \frac{1}{4} x^{7} y^{5}

Multiply fractions:

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

= \frac{1 \cdot 16 x ^{7} y ^{5}}{4}

Multiply the numbers:

1 \cdot 16 = 16

= \frac{16 x ^{7} y ^{5}}{4}

Divide the numbers:

\frac{16}{4} = 4

= 4 x^{7} y^{5}

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