Use rational exponents to write 4√6 * 3√7 as a singular expression.
How in the world do I write this??
To write the expression 4√6 * 3√7 as a singular expression using rational exponents, we need to transform the radicals (√) into fractional exponents.
Step 1: Simplify the radicals (√) if possible.
√6 can be simplified as 6^(1/2).
√7 can be simplified as 7^(1/2).
Step 2: Rewrite the expression using the simplified radicals.
4√6 * 3√7 becomes 4(6^(1/2)) * 3(7^(1/2)).
Step 3: Apply the exponent rules for multiplying exponents.
When we have the same base raised to different exponents and are multiplying them, we add the exponents.
4(6^(1/2)) * 3(7^(1/2)) becomes 4 * 3 * 6^(1/2) * 7^(1/2).
Step 4: Multiply the coefficients (numbers) and simplify the exponents.
4 * 3 is 12.
The final expression in a singular expression with rational exponents is:
12 * (6^(1/2)) * (7^(1/2)).