Calculate each value mentally. (0.25^3)(400^3)

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression, parentheses 0.2 squared times new parentheses 160 squared. Were asked to compute this cognitively. So without a calculator. Well, the first thing I notice here is this 0.2. We could rewrite that as 1/5 and that's still 1/ squared times 160 squared. And now we can recall the quotient to power rule from previous lessons. The quotient to power rule tells us that if we have a fraction Then the whole thing is raised to an exponent, then that exponents can be applied to both the numerator and the denominator. Or in other words we can rewrite this one squared over five squared. And yes, that's still times 160 squared. And now we can simplify what's in the numerator because we know that one squared equals one. So I'm going to give myself a little more room. We have 1/5 squared times 160 squared. And now we could rewrite this 160 squared over one. And now we can multiply straight across for our enumerators and straight across for our denominators, one times 160 squared is 160 squared and five squared times one is five squared. And now look here, is that quotient to power rule again. But this time in reverse. Now we have the same exponents. Someone into change colors. We've got the same exponents in both the numerator and the denominator and we can pull those outside of the parentheses. So we could rewrite this as parentheses 160 over five squared and now we can do the division that's inside those parentheses, 160 divided by five is squared and 32 squared equals 1024. We look at our answer choices and this matches with answer choice. C. Well done, we'll catch you on the next one.

Calculate each value mentally. (0.25^3)(400^3)

Key Concepts

Exponents

Properties of Exponents

Mental Math Techniques

Watch next