Simplify 4^13 divided by 3^-5 using the quotient rule of exponents
To simplify the expression 4^13 divided by 3^-5 using the quotient rule of exponents, we subtract the exponent of the denominator from the exponent of the numerator.
Using the quotient rule, we have:
4^13 / 3^-5 = 4^13 * 3^5
Now, we can simplify each base raised to a power:
4^13 * 3^5 = (2^2)^13 * 3^5
= 2^(2*13) * 3^5
= 2^26 * 3^5
Now we can write this as a single exponent:
= 2^26 * 3^5
= 67,108,864 * 243
Multiplying these two numbers, we get:
= 16,293,536,352
that answer is incorrect
To simplify the expression 4^13 divided by 3^-5 using the quotient rule of exponents, we need to subtract the exponents.
According to the quotient rule, when dividing two numbers with the same base, the exponents are subtracted.
Let's apply this rule to our expression:
4^13 / 3^-5 = 4^(13 - (-5))
Now, we can simplify the exponent:
4^(13 - (-5)) = 4^(13 + 5) = 4^18
Therefore, the simplified expression is 4^18.
Apologies for the incorrect answer. Let's correct the calculation.
Using the quotient rule of exponents, we subtract the exponent of the denominator from the exponent of the numerator.
4^13 / 3^-5 = 4^13 * 3^5
To simplify, we can evaluate each base raised to its respective exponent:
4^13 * 3^5 = 4^13 * (3^5 / 1^5)
Since any number raised to the power of 1 is itself, we can simplify the denominator:
4^13 * (3^5 / 1) = 4^13 * 3^5
Now, we can multiply the bases:
4^13 * 3^5 = (2^2)^13 * 3^5
Applying the power rule to simplify further:
= 2^(2*13) * 3^5
= 2^26 * 3^5
Now we can write this as a single exponent:
= 2^26 * 3^5
To compute this, we multiply the numbers:
= 67,108,864 * 243
= 16,323,739,392
Therefore, 4^13 / 3^-5 simplifies to 16,323,739,392.