To calculate \(4^{13}\) divided by \(3^{-5}\), let's first simplify each part separately:
\(4^{13}\) means 4 multiplied by itself 13 times.
\(3^{-5}\) is the negative exponent, which means 1 divided by the base raised to the positive exponent, so it translates to \(\frac{1}{3^5}\).
Now let's divide \(4^{13}\) by \(3^{-5}\):
\(4^{13} \div 3^{-5} = 4^{13} \times \frac{1}{3^{-5}} = 4^{13} \times 3^{5}\).
Since the bases are different, we cannot simplify the expression by subtracting the exponent directly. We need to evaluate each expression and then divide them:
\(4^{13}\) = \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\)
\(3^5\) = \(3 \times 3 \times 3 \times 3 \times 3\)
The exact evaluations will be very large numbers:
- \(4^{13}\) is 67,108,864.
- \(3^5\) is 243.
Now divide:
\(\frac{67,108,864}{243}\)
To get the quotient, perform the division:
67,108,864 รท 243 = 276,190.4 (approximately)
So \(4^{13} \div 3^{-5}\) is approximately 276,190.4. This is a decimal representation, and your specific requirement may call for leaving it as a fraction or a mixed number. If you need the result in its exact form without decimals, you must perform the division without rounding to retain the fraction part. Alternatively, you could also represent the answer in scientific notation if the absolute precision is not a concern.
4^13 divided by 3^-5
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