Simplify:
(4xy^-6)^-3

(4^-3)(x^-3) y^(18)

or

y^18/ (64 x^3)

Step-by-step explanation:

(4xy^-6)^-3

Distribute the exponent to all terms in the parentheses

(4^-3)(x^-3) (y^-6)^-3

a^ b^c = a^ (b*c)

(4^-3)(x^-3) y^(-6*-3)

(4^-3)(x^-3) y^(18)

If we do not want negative exponents

a ^ -b = 1/ a^b

y^18/( 4^3 x^3)

y^18/ (64 x^3)

μ > 21.21

Test statistic = 1.217

Kindly check explanation for more details

Step-by-step explanation:

The null hypothesis, H0 : μ = 21.21

Alternative hypothesis, H1 : μ > 21.21

The test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(21.212 - 21.21) ÷ (0.01 / √2)

= 1.217

The critical value :

From the t distribution :, one tailed = 2.434

Decision region :

Reject H0 if test statistic > critical value

1.217 < 2.434 ; We fail to reject the null ` ; and conclude that there is not enough evidence to support the claim.