All of the following expressions are equivalent to 6 x 15^t. However, only one has been rewritten using exponent property #3, bx/by = b^x−y.
a) 6/15^-t
b) 2 x 3^t+1 x 5^t
c) (6^t x 15^t)/6^t-1
d) 6 x 15^12t x 15^-t
To determine which expression has been rewritten using exponent property #3, bx/by = b^x−y, we need to simplify each expression and compare them to the original expression, 6 x 15^t.
Let's analyze each option:
a) 6/15^-t
To rewrite this expression using exponent property #3, we would need to rewrite the numerator and denominator with the same base. However, in this case, the numerator has a base of 6, while the denominator has a base of 15. So this expression does not match the required form.
b) 2 x 3^t+1 x 5^t
In this expression, we have two bases, 3 and 5, raised to different powers. Exponent property #3 requires the same base for numerator and denominator. Therefore, this expression does not match the required form.
c) (6^t x 15^t)/6^t-1
In this expression, we have both 6^t and 15^t in the numerator, raised to the same power. Exponent property #3 states that when dividing with the same base, we subtract the exponents. In this case, the numerator can be rewritten as (6 x 15)^t = 90^t. However, the denominator, 6^t-1, does not match the required form. Therefore, this expression does not match the required form.
d) 6 x 15^12t x 15^-t
This expression involves 15 raised to different powers, which cannot be directly combined using exponent property #3. Therefore, this expression does not match the required form.
None of the given expressions match the required form of rewriting using exponent property #3.