Question

Write 5^3 x √5 as a single power of 5

Answer 1

To express 5^3 x √5 as a single power of 5, rewrite √5 as 5^(1/2), and then add the exponents to get 5^(3 + 1/2), which simplifies to 5^(7/2).

Step-by-step explanation:

To write 5^3 x √5 as a single power of 5, we need to express the square root of 5 as a power with a fractional exponent. We know that x² = √x, and therefore √5 can be re-expressed as 5^(1/2). Combining this with 5^3, we get:

5^3 x 5^(1/2)

Now, according to the laws of exponents, when we multiply expressions with the same base, we add their exponents. This gives us:

5^(3 + 1/2) = 5^(3.5) or 5^(7/2)

This represents the single power of 5 that is equivalent to the original expression.

Answer 2

√5 = 5^(1/2)

Multiplying two number with the same base has as result a number with the same base and the sum of the exponents so:

1/2 + 3 = 7/2
which means
5^3 x 5^(1/2) = 5^(7/2)