Question

Which expression is equivalent to 1.5 raised to the fifth power divided by 0.7 raised to the fourth power, all raised to the third power?

1.5 raised to the fifteenth power divided by 0.7 raised to the twelfth power
1.5 raised to the eighth power divided by 0.7 raised to the seventh power
2.13
2.115

Answer 1

1.5 raised to the third power, which is 1.5^3 is the correct answer.

Explanation:

First, let's simplify the expression inside the parentheses: 1.5^5 divided by 0.7^4.

To divide two powers with the same base, we subtract the exponents. So, 1.5^5 divided by 0.7^4 is equal to 1.5^(5-4) which simplifies to 1.5^1.

Now, let's raise 1.5^1 to the third power. When we raise a number with an exponent to another exponent, we multiply the exponents. So, 1.5^1 raised to the third power is equal to 1.5^(1*3) which simplifies to 1.5^3.

Therefore, the expression is equivalent to 1.5 raised to the third power, which is 1.5^3.