Please help with 4 algebra questions!!

Evaluate 1/2a^4b^2 for a = –2 and b = 4. (1 point)

A)2 ----------------

B)1/2

C)3

D)4

Is the following statement always, never, or sometimes true?

A number raised to a negative exponent is negative. (1 point)

A)always

B)never

C)sometimes ----------------

Simplify (4xy^2)^3(xy)^5 (1 point)

A)64x^8y^11

B)64x^15y^30

C)12x^2y^11

D)12x^8y^11 ----------------

Simplify (2t^3)^3(0.4r)^2 (1 point)

A)3.2r^2

B)1.28r^2/t^-6 ----------------

C)1.28r^2/t^9

D)0.8r^2/t^-6

Question

Answered

Verified Answer :

Anonymous Anonymous · Answer 1 · 2019-02-12T08:16:14-05:00

Solution:

Law of indices

\(1.a ^m \times a ^n= a^{m+n} 2. \frac{a^m}{a^n}=a^{m-n} 3. a^m \times b^m=(ab)^{m}\)

1.

\(\frac{1}{2}\times a^4\times b^2\\\\ =\frac{1}{2}\times(-2)^4\times(4)^2\\\\ =\frac{1}{2}\times2^4\times (2^2)^2\\\\ =2^{4+4-1}\\\\ 2^7=128\)

2.

A number raised to a negative exponent is negative.=False Statement

because, \(a^{-m}=\frac{1}{a^m}\)

=Option (C) sometimes because \((-3)^{-3}=\frac{-1}{27}\)

3.

\((4xy^2)^3(xy)^5 =4^3\times x^3 \times x^5\times y^6 \times y^5\\\\ =64 x^8 y^{11}\)

=Option (A)

4.

\(= (2t^3)^3(0.4r)^2\\\\= 2^3\times (t^3)^3*(0.4)^2*r^2\\\\= 8 *0.16 *t^9*r^2\\\\=1.28 t^9 r^2\)