Simplifying Expressions with Negative Exponents

The video tutorial explains how to simplify expressions with negative exponents, specifically focusing on the expression two-thirds raised to the power of negative two. It covers two main methods: using the power to power rule and converting negative exponents to positive by moving terms across the fraction bar. The tutorial also demonstrates the reciprocal rule, showing that the expression can be simplified to nine-fourths using either method. The video emphasizes understanding exponent rules and applying them to achieve the same simplified result.

What is the power to power exponent rule?

• a^m * a^n = a^(m+n)

• a^m / a^n = a^(m-n)

• (a^m)^n = a^(m*n)

• a^m + a^n = a^(m+n)

How do you simplify (2/3)^-2 using the power to power rule?

• Multiply the exponents and keep the fraction the same

• Add the exponents and invert the fraction

• Multiply the exponents and invert the fraction

• Add the exponents and keep the fraction the same

What happens to the exponent when a term crosses the fraction bar?

• The exponent becomes positive

• The exponent doubles

• The exponent becomes zero

• The exponent becomes negative

How do you convert (2/3)^-2 to positive exponents?

• Keep both in the denominator

• Keep both in the numerator

• Move 2^-2 to the numerator and 3^-2 to the denominator

• Move 2^-2 to the denominator and 3^-2 to the numerator

What is the reciprocal rule for exponents?

• a/b raised to -m is equal to b/a raised to -m

• a/b raised to -m is equal to a/b raised to m

• a/b raised to -m is equal to b/a raised to m

• a/b raised to -m is equal to a/b raised to -m

How do you apply the reciprocal rule to (2/3)^-2?

• Convert it to (2/3)^-2

• Convert it to (2/3)^2

• Convert it to (3/2)^-2

• Convert it to (3/2)^2

What is the result of (3/2)^2?

• 3/2

• 2/3

• 4/9

• 9/4

Which method can be used to simplify (2/3)^-2?

• Only the reciprocal rule

• Only the power to power rule

• Neither power to power nor reciprocal rules

• Both power to power and reciprocal rules

What is the simplified form of (2/3)^-2?

• 9/4

• 4/9

• 2/3

• 3/2

What is the importance of expressing answers with positive exponents?

• It is required for all mathematical expressions

• It is only necessary for fractions

• It makes calculations easier

• It is a standard mathematical practice