Step-by-step explanation:
given
[tex](1.5 \times {10}^{4} )(8 \times {10}^{8} )[/tex]
in order to make multiplication easier we need to change the 1.5 into a whole number form.
thus
[tex](15 \times {10}^{ - 1} \times {10}^{4} )(8 \times {10}^{8} )[/tex]
[tex] = (15 \times {10}^{4 - 1} )(8 \times {10}^{8} )[/tex]
First law of indices applied there
=(15×10^3)(8×10^8)
=(15×8)(10^3×10^8)
=120×10^3+8 ( first law of indices, which states that , numbers of the same base multiplying each other, take one of the base and add the exponent. and clearly both 15 and 8 are in base 10
=120×10^11
=1.20×10^2 ×10^11
=1.20×10^11+2
=1.20×10^13
so the answer is alt B
