Quotient Rule of Exponents Practice
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Simplify 4^13÷3^−5 (1 point)
To simplify the expression 4^13 ÷ 3^(-5), we can apply the quotient rule of exponents, which states that a^(m-n) = a^m / a^n.
In this case, we have 4^13 ÷ 3^(-5). Applying the quotient rule, we can rewrite the expression as:
4^13 / 3^(-5)
Now, let's simplify each term by applying the product rule of exponents.
4^13 = (2^2)^13 = 2^(2*13) = 2^26
3^(-5) = 1 / 3^5 = 1 / (3^2 * 3^3) = 1 / (9 * 27) = 1 / 243
Now, we can substitute these values back into the expression:
2^26 / 1 / 243
When dividing by a fraction, we can invert the fraction and multiply, so we have:
2^26 * 243
To simplify further, we can rewrite 243 as 3^5:
2^26 * 3^5
Now, we add the exponents when multiplying:
2^26 * 3^5 = 2^(26+5) * 3^5 = 2^31 * 3^5
So, the simplified expression is 2^31 * 3^5.
To simplify the expression 4^13 ÷ 3^(-5), we can use the quotient rule of exponents.
According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents.
4^13 ÷ 3^(-5) = 4^13 * 3^5 (since dividing by a negative exponent is equivalent to multiplying by the positive exponent)
Now, to simplify further, we can evaluate the powers separately.
4^13 = 67108864 (you can use a calculator or compute it manually by multiplying 4 thirteen times)
3^5 = 243 (you can calculate this by multiplying 3 five times)
Therefore, 4^13 ÷ 3^(-5) simplifies to 67108864 ÷ 243 = 276416.