Solve sqrt(10^(-7)) * sqrt(26)

Question

Calculate the value

\frac{65}{5000}

Alternative Form

\approx 0.001612

Evaluate

1 0^{- 7} \times 26

Simplify the root

More Steps

Evaluate

1 0^{- 7}

Express with a positive exponent using a^{- n} = \frac{1}{a ^{n}}

\frac{1}{1 0 ^{7}}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{1 0 ^{7}}

Simplify the radical expression

\frac{1}{1 0 ^{7}}

Simplify the radical expression

More Steps

Evaluate

1 0^{7}

Rewrite the exponent as a sum where one of the addends is a multiple of the index

1 0^{6 + 1}

Use a^{m + n} = a^{m} \times a^{n} to expand the expression

1 0^{6} \times 10

The root of a product is equal to the product of the roots of each factor

1 0^{6} \times 10

Reduce the index of the radical and exponent with 2

1 0^{3} 10

\frac{1}{1 0 ^{3} 10}

Rewrite the expression

\frac{1}{1000 10}

Multiply by the Conjugate

\frac{10}{1000 10 \times 10}

Multiply the numbers

More Steps

Evaluate

100010 \times 10

When a square root of an expression is multiplied by itself,the result is that expression

1000 \times 10

Multiply the terms

10000

\frac{10}{10000}

\frac{10}{10000} 26

Multiply the numbers

\frac{10 \times 26}{10000}

Multiply the numbers

More Steps

Evaluate

10 \times 26

The product of roots with the same index is equal to the root of the product

10 \times 26

Calculate the product

260

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 65

Write the number in exponential form with the base of 2

2^{2} \times 65

The root of a product is equal to the product of the roots of each factor

2^{2} \times 65

Reduce the index of the radical and exponent with 2

265

\frac{2 65}{10000}

Solution

\frac{65}{5000}

Alternative Form

\approx 0.001612

Show Solution