**HP 41/DM41L and TI-60X: Exponentiation of Large Numbers**

**But Why a Program when we have Button?**

This is true. What this program does is allow for calculation of y^x when results in answers greater than 9.999999999 * 10^9. The number is broken up into the form:

mantissa * 10^exponent

Let n = y^x. Then:

n = y^x

Taking the logarithm of both sides:

log n = log (y^x)

log n = x log y

A number can be split into its fractional and integer part:

log n = frac(x log y) + int(x log y)

Take the antilog of both sides:

n = 10^( frac(x log y) + int(x log y) )

n = 10^( frac(x log y) ) * 10^( int(x log y) )

where

mantissa = 10^( frac(x log y) )

exponent = int(x log y)

**HP 41/DM 41L Program BIGPOW**

Input:

Y stack: y

X stack: x

Output:

Y: mantissa (shown first)

X: exponent

01 LBL T^BIGPOW

02 X<>Y

03 LOG

04 *

05 ENTER↑

06 FRC

07 10↑X

08 STOP

09 X<>Y

10 INT

11 RTN

**TI-60 Program: Big Powers**

Input:

Store y in R1 and x in R2

Output:

R1 = mantissa (shown first), R2 = exponent

(Step, Key Number, Key)

00, 71, RCL

01, 02, 2

02, 65, *

03, 71, RCL

04, 01, 1

05, 43, log

06, 95, =

07, 61, STO

08, 02, 2

09, 78, Frac

10, 12, INV

11, 43, log

12, 61, STO

13, 01, 1

14, 13, R/S

15, 71, RCL

16, 02, 2

17, 79, Intg

18, 13, R/S

19, 22, RST

**Examples**

Example 1: 25^76. y = 25, x = 76

Result:

Mantissa = 1.75162308

Exponent = 106

25^76 ≈ 1.75162308 * 10^106

Example 2: 78^55.25, y = 78, x = 55.25

Result:

Mantissa = 3.453240284

Exponent = 104

78^55.25 ≈ 3.543240284 * 10^104

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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