How do you express t^-6 as a positive exponent?

Jan 19, 2018

${t}^{- 6} = \frac{1}{t} ^ 6$ See explanation.

Explanation:

If an expression has a negative exponent then to transform it to positive exponent you have to calculate the reciprocal of the expression:

${a}^{- b} = \frac{1}{a} ^ b$

Now why is this true?
Well, let's use algebra.

Remember that ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$

Now, ${a}^{b} \cdot {a}^{- b} = {a}^{b - b} \implies {a}^{0} = 1$
So we have ${a}^{b} \cdot {a}^{-} b = 1$ We manipulate this to:
${a}^{- b} = \frac{1}{{a}^{b}}$