Question

express in the simplest exponential form (I) 16 * 64 (II) 25*125 (III) 128 divided by 32​

Answer 1

Answer:

1)4^2*4^3

2) 5^2*5^3

3) 2^7/2^5

Answer 2

$i)\ 16 \times 64 = 4^5$

$ii)\ 25 \times 125 = 5^5$

$iii)\ \frac{128}{32} = 2^2$

Solution:

Given that,

We have to express in simplest exponential form

Exponential form means a numeric form involving exponents

i)

$16 \times 64\\\\4^2 \times 4^3\\\\We\ know\ that\\\\\boxed{ a^m \times a^n = a^{m+n}}\\\\Therefore\\\\4^2 \times 4^3 = 4^{2+3} = 4^5\\\\Thus,\\\\16 \times 64 = 4^5$

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ii)

$25 \times 125\\\\5^2 \times 5^3\\\\Similarly,\\\\5^2 \times 5^3 = 5^{2+3} = 5^5\\\\Thus\\\\25 \times 125 = 5^5$

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iii)

$\frac{128}{32}\\\\\frac{2^7}{2^5}\\\\We\ know\ that\\\\\boxed { \frac{a^m}{a^n} = a^{m-n}}\\\\\\Therefore\\\\\frac{2^7}{2^5} = 2^{7-5} = 2^2\\\\Thus\\\\\frac{128}{32} = 2^2$

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