Express 3-5- 3-4 as a power of 3 with positive exponent-

We know that, a^m × a^n = a^m+n ⇒ 3^ 5× 3^ 4 = 3^ 5+( 4) = 3^ 5 4=3^ 9 Now, We also know that, nbsp;a^ m = 1/a^m So, we can write 3^ 9 as 1/3^9. Hence, nbs ...

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Mathematics

Exponents

Express 3-5× ...

Question

Express $3^{- 5} \times 3^{- 4}$ as a power of 3 with positive exponent.

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Solution

We know that, $a^{m} \times a^{n} = a^{m + n}$
$\Rightarrow 3^{- 5} \times 3^{- 4} = 3^{- 5 + (- 4)} = 3^{- 5 - 4} = 3^{- 9}$
Now,
We also know that, $a^{- m} = \frac{1}{a^{m}}$
So, we can write $3^{- 9}$ as $\frac{1}{3^{9}}$ .
Hence, $3^{- 5} \times 3^{- 4}$ can be represented as $\frac{1}{3^{9}}$ where power of 3 is positive.

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Express 3−5×3−4 as a power of 3 with positive exponent.

We know that, am×an=am+n ⇒ 3−5×3−4=3−5+(−4)=3−5−4=3−9 Now, We also know that, a−m=1am So, we can write 3−9 as 139. Hence, 3−5×3−4 can be represented as 139 where power of 3 is positive.

Express $3^{- 5} \times 3^{- 4}$ as a power of 3 with positive exponent.