quotient rule of exponents practice simplify 4^13 / 3^-5
To simplify the expression 4^13 / 3^-5 using the quotient rule of exponents, we can rewrite the expression as:
4^13 * 3^5
Now, we use the product rule of exponents to simplify:
= 4^13 * (3^2 * 3^3)
= 4^13 * 3^2 * 3^3
Now, we can simplify further by multiplying the coefficients and adding the exponents:
= (4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4) * 3^2 * 3^3
= 8,192 * 3^2 * 3^3
= 8,192 * 9 * 27
= 18,874,368.
To simplify the expression (4^13) / (3^-5) using the quotient rule of exponents, we need to remember the rule:
a^m / a^n = a^(m - n)
In our expression, a = 4, m = 13, and a = 3, n = -5. Plugging in these values, we get:
4^13 / 3^-5 = 4^(13 - (-5))
Now let's simplify the exponent:
13 - (-5) = 13 + 5 = 18
So, the expression simplifies to:
4^13 / 3^-5 = 4^18
To simplify the expression 4^13 / 3^(-5) using the quotient rule of exponents, you need to understand the rule itself.
The quotient rule of exponents states that when you divide two powers with the same base, you subtract the exponents. Mathematically, it can be written as:
a^m / a^n = a^(m - n)
Now let's apply the quotient rule to the given expression: 4^13 / 3^(-5).
Step 1: Retain the base (in this case, both bases are different: 4 and 3). To solve this, we need to express both bases in terms of the same number (in this case, it'll be 2 as both numbers are divisible by 2).
Step 2: Convert the expression to exponent form. Remember that a number raised to the power of -n is equivalent to 1 divided by a number raised to the power of n. So, we can rewrite the expression as:
(4^13) / (1 / 3^5)
Step 3: Apply the quotient rule. We can now divide and subtract the exponents:
4^13 / (1 / 3^5) = 4^13 * 3^5
Since the bases are different, we cannot simplify the expression any further. So, the final answer is:
4^13 * 3^5